"RF excited CO2 lasers are widely used in industry. They provide relatively high power discharge levels while maintaining compactness, simplicity, and durability with respect to other competing laser technologies. To attain high power levels in the range of 5-10 KW, lasers with large electrode areas have to be designed. Unfortunately, due to the large electrode length requirements, transmission line effects make the discharge loading nonlinear, adversely affecting the efficiency of the CO2 laser. A standard approach to linearize the discharge loading is to introduce shunt inductors across the length of the electrodes in an effort to counter the capacitive nature of the discharge behavior. This thesis investigates and improves the theoretical models found in the literature in an effort to predict the discharge non-uniformity and allow for multiple shunt inductors installation. Specifically, we discuss the coupling of a CO2 laser discharge model with an electrical circuit solving scheme and how it can be characterized as one dimensional (1-D) and two dimensional (2-D) systems. The 1-D system is modeled using transmission line (TL) theory, where as the 2-D system is modeled using a finite difference time domain (FDTD) scheme. All our models were implemented in standard MATLAB code and the results are compared with those found in the literature with the goal to analyze and ascertain model limitations."